Abstract
A positive step function f can be written uniquely in the form f = Σa•1 A • a linear combination, with positive pairwise distinct coefficients, of indicator functions of a finite disjunct sequence of measurable sets. Define the integral of f on S with respect to λ, using this representation of f, by
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© 1994 Springer Science+Business Media New York
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Doob, J.L. (1994). Integration. In: Measure Theory. Graduate Texts in Mathematics, vol 143. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0877-8_7
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DOI: https://doi.org/10.1007/978-1-4612-0877-8_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6931-1
Online ISBN: 978-1-4612-0877-8
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